We report here the recent developments in the SIS calibration and the analysis
software. Three topics are addressed: a new method of DFE correction, low
energy calibration, and the non-uniform CTI. Some of the new calibration
results have been incorporated in the FTOOLS version 3.5.

1 New method of DFE correction

It is crucial in spectral analysis to use the correct gain (i.e., slope and
offset of the energy scale) of a detector. However, the energy scale offset
(and maybe slope) of the SIS is not simple, and may depend on observation mode
and time. We have developed new DFE (dark frame error) correction software to
minimize the systematic effects on the energy scale offset. As explained
below, the new software affects not only the energy scale offset but also the
detection efficiency. We first explain the definition of zero of the energy
scale, and then the algorithm of the new DFE correction software. The impact
on the spectral analysis is explained afterward. This new DFE correction
software has been implemented and is available from version 3.5 of FTOOLS.

1.1 Definition of zero

We use the pulse height distribution of pixels to define the zero energy scale.
When neither an X-ray photon or charged particle hits the CCD and the radiation
damage of the CCD is negligible, the pulse height distribution of pixels has an
approximately gaussian profile. This is because the dark current is negligible
and the pulse height distribution is determined by the readout noise. In this
case, the definition of the zero energy scale is the center of the gaussian.

The zero energy scale is calculated on board for each 16 x 16 pixel region. To
avoid contamination from the X-ray and particle events, a truncated mean is
used to estimate the center of the pulse height distribution. The running
average of the truncated mean of several consecutive exposures is calculated to
smooth the statistical fluctuations. This running average is called a dark
frame, and is used on board to correct the pulse height of each pixel. Because
it takes at least several tens of seconds to update the dark frame, the dark
frame calculated on board may not catch up with any rapid changes of the light
leak, such as due to the day/night transition. The difference between the
on-board dark frame and the true zero is called dark frame error (DFE), which
may be corrected in the ground processing. Explanation of DFE and it's
correction scheme is found in [1].

When the radiation damage becomes significant, the pulse height distribution is
no longer a gaussian, but rather has a prominent tail toward higher energies.
This is explained by the large increase of dark current in some pixels due to
the radiation damage. This asymmetrical pulse height distribution is called
RDD (residual dark distribution), because the asymmetry remains even after the
DFE correction. Definition of the zero energy scale is somewhat arbitrary for
the asymmetrical distribution of RDD. However, RDD has various effects on the
SIS performance, and the effect is highly dependent on the definition of zero
that is used. Thus we should define a zero energy scale that minimizes the
impact on the SIS performance. Even when we use such a definition of zero,
some effects still remain on the SIS performance that must be included in the
SIS response matrices.

Before presenting the definition of zero, we introduce several terms related to
the RDD.

Figure 1: Schematic pulse height distribution of CCD pixels under the
effect of RDD. The pulse heights corresponding to the peak, the truncated mean
and the global mean of the distribution are indicated.

Global mean
This is a mean value of the pulse height calculated from the pulse height data
of all pixels.

q x RDD
(1)

where RDD
[1]
is a pulse height distribution under the RDD effect normalized to unity. This
is a new zero level definition adopted in FTOOLS version 3.5 and can be
calculated with the new "faintdfe" (zerodef = 1).

Truncated mean
This is a self-consistent solution of the following formula:

q x RDD
(2)

This corresponds to the on board zero when there is no light leak. The new
"faintdfe" uses this definition when zerodef = 2.

Peak This is the pulse height at which the distribution peaks. Old
"faintdfe" effectively searches for the peak of the
distribution. The new "faintdfe" uses this definition when zerodef = 0.

These means/peak are schematically explained in figure 1. The old version of
"faintdfe" effectively looks for the peak of distribution, and adjust the
energy scale such that the peak becomes zero. If we use this zero, more and
more pixels tend to have higher pulse height with the increase of the radiation
damage. This has basically two effects on the SIS performance [2]:

Such systematic effects will be reduced by using the "global mean" as the zero
energy scale.

1.2 Energy scale offset

We show in figure 2 the history of the Ni line energy in the SIS internal
background. Two plots are shown in the figure; one uses the peak as the zero
in the DFE correction, and the other uses the global mean as zero. Because the
RDD effect is most significant in 4 CCD mode [2], the difference of the two
plots is most significant in 4 CCD mode data. If we adopt the peak as zero of
the energy scale, the Ni line energy gradually increases with time after the
CTI correction. This is an artifact due to the RDD effect. If we adopt the
global mean as zero, this effect is hardly visible. The systematic effect in
the energy scale offset becomes very small with the new definition of zero.

Figure 2: Long-term history of the Ni line energy in the internal
background of SIS. The first panel is SIS-0 and the second panel SIS-1. Filled
symbols represent data processed using the global mean as zero, and open
symbols those processed with the peak as zero, in the course of DFE
correction.

1.3 Detection efficiency

We show in figure 3 simulated energy spectra of 3C273 assumed to be observed in
4 CCD mode. The data are processed using the new "faintdfe" in three different
ways: one uses the peak as zero, another uses the truncated mean as zero, and
the other the uses global mean as zero. The difference in the detection
efficiency is apparent. The decrease of the detection efficiency is largest
when we use the peak as zero, and is smallest when we use the global mean as
zero.

Figure 3: Simulated spectra of 3C273 in 4 CCD mode at the epoch of Nov.
30, 1997. The data are processed by the new "faintdfe" with three different
options. One uses the global mean as zero (solid line), another uses the
truncated mean (dotted), and the third the peak (dashed). A reduction in the
detection efficiency is minimized when the global mean is used as the zero
level. Bright mode data uses the truncated mean method.

If we adopt the peak as the zero energy scale, many pixels tend to have high
pulse heights due to the high energy tail of the RDD. Some pixels have even
higher pulse height than the split threshold (40 ADU). With such pixels, a
single event may be falsely classified as a split event (grade 2, 3, 4), and a
split event as a higher grade event (grade 5, 6, 7). Thus, an X-ray event
tends to be classified as a non X-ray event and this reduces the quantum
detection efficiency. As seen from the figure, this reduction of the detection
efficiency is almost energy independent.

If only the faint mode data are being processed, zerodef = 1 (global mean)
should be used. This will minimize the RDD effect. However, because the RDD
effect is not significant in 1-CCD mode data at present, different choice of
zero will not produce a major difference in 1-CCD mode data.

When mixing the Faint mode and Bright mode data, there are several choices.

(i) If most of the data are in Faint mode, you may just discard the Bright mode
data.

(ii) If the Bright mode data are taken during the satellite night, you can use
zerodef = 2 to correct the DFE of the Faint mode data and add in the Bright
mode data, because DFE during the satellite night is stable and predictable.
"Faintdfe" with zerodef = 2 will correct DFE of the Faint mode data and adjust
the zero energy scale to that of the Bright mode data, so that the Faint and
the Bright mode data can be added consistently. Of course, you need to use
response matrices of the Bright mode data for such data. When an observing
plan includes the use of Bright mode, the mission operation team at ISAS
usually tries to allocate Bright mode to the satellite night time.

(iii) If most of the Bright mode data are taken during the satellite day time
and you want to combine Bright mode and Faint mode data, there is no simple
choice. Try several different methods, i.e., zerodef = 1, zerodef = 2,
or no DFE correction, to estimate the energy scale uncertainties.

(iv) The option of zerodef = 0 is not recommended, it is supplied for backward
compatibility.

2 Low energy cal

In this section, we outline the calibration made to determine the detection
efficiency of SIS (plus XRT) at low energies. To determine the low energy
efficiency, we consider (1) the thermal shield of XRT, (2) the effective area
of XRT, (3) the optical blocking filter of SIS, and (4) the dead layer of CCD.
In addition, radiation damage of the CCD changes the apparent detection
efficiency as explained in the previous section. We cannot use the flight data
to independently calibrate the 4 items listed. For example, both the thermal
shield and the optical blocking filter have an aluminum coating, and their
thickness cannot be determined separately. Thus, we calibrate just the total
efficiency, not the efficiency of each component.

2.1 Calibration with 3C273

We assumed that the XRT response (including the effective area) and the GIS
response are well calibrated using the Crab and other data. Because the Crab
is too bright for SIS to get useful data, we used 3C273 to calibrate the SIS.
The >1 keV energy spectrum of 3C273 is approximately a power law, but the
slope is time variable. Thus we calibrated SIS to give the same energy index
as that of GIS using the data from exactly the same time interval for SIS and
GIS. Because the observation of 3C273 was done in December 1993, the effect of
the radiation damage should be small, but cannot be neglected. Finally, the
energy spectrum of 3C273 may not be a power law; we will discuss this point
later.

The method of SIS calibration with 3C273 data is as follows. We have 4
pointings in the 3C273 observations. The source was put on each chip and the
data were obtained in 1-CCD Faint mode with that chip.

1. Calculate the GIS spectrum of 3C273 for each set of data. The energy
spectrum is fitted with a power law above ~3 keV and the power law index is
determined for each pointing.

2. Calculate the SIS energy spectra of 3C273 using the latest calibration
data. DFE and CTI corrections are carefully made.

3. Using the SIS energy spectrum above ~3 keV to calibrate the depletion layer
thickness of each chip by adjusting it

to give the same energy index as the GIS spectrum.

4. The combined low energy absorption by nitrogen, oxygen, silicon and
aluminum are adjusted such that a simple

power law modified by the Galactic absorption fits the data. Absorption by
hydrogen and carbon is effectively

adjusted by nitrogen.

Figure 4: Flow of SIS calibration method with the 3C273 data. The
above method is illustrated in figure 4.

The depletion layer thickness determined with the 3C273 data is between 26--33
um
and is consistent with the ground calibration (3). We show in figure 5 an
example of detection efficiency of SIS calibrated using 3C273 data. Two
efficiency curves are shown in the figure. One is based on the ground
calibration data and telescope ray tracing. The other uses the flight
calibration with the 3C273 data. Although there is a difference in the
detection efficiency between the two sets of calibrations, it is small, at up
to ~10% level. The low energy efficiency we obtained is on average slightly
lower than that of the ground calibration. Possible origins of this difference
are: (1) the uncertainty of the XRT, GIS and SIS responses; (2) the radiation
damage of SIS; (3) an accumulation of hydrocarbons on XRT or the optical
blocking filter of SIS; (4) the calibration error of the thickness of the
thermal shield, the optical blocking filter or the dead layer of the CCD. It
is noteworthy that, if a soft excess is present in 3C273, the quantum detection
efficiency at low energies should be reduced further. Further investigations
are underway to understand these discrepancies.

2.2 Features around 0.5 keV

A power law (modified by the Galactic absorption) model generally fits the
observed energy spectra of 3C273 well, but some residual structures remain
around 0.5 keV. There is an oxygen edge structure at 0.532 keV in the SIS
detection efficiency, and the residual structure of 3C273 is most significant
around this edge structure. Thus the residual is suspected to be an artifact
due to a slight difference between the observed and model edge energy.

It is essential to use the correct energy scale (offset and slope) to reproduce
the edge structure accurately. However, the apparent edge energy of oxygen in
the observed spectra may vary from observation to observation mainly for two
reasons: one is the error of DFE correction and the other is the uncertainty
of CTI. The optical light leak changes with time, sometimes as rapidly as
102 sec.

The DFE correction tries to remove such time-dependent changes of energy scale
offset due to the light leak, but its accuracy is limited by the available
number of events. CTI may also change from observation to observation
depending on the X-ray flux of the source. Moreover, the optical light leak,
which depends on the satellite attitude, tends to reduce the CTI , which
changes the energy scale slope (and possibly the offset). Thus the apparent
oxygen edge energy in the spectrum varies from observation to observation.
This variation, which may be as small as 10 eV, has small effects at energies
where the detection efficiency does not have sharp structures, but produces
artificial structures at energies where the efficiency changes discontinuously,
such as the oxygen edge and the Si edge. Because it is difficult to correct
for the apparent variation of the edge energy in the observed spectra with
enough accuracy, artificial structure around 0.5 keV is difficult to remove at
present.

We have analyzed the structure around 0.5 keV for various sources. It is found
that the structure becomes prominent below ~0.6 keV and the amplitude of
structure is typically ~10% (see also the next subsection). Because the
structure arises from the slight deviation of the energy scale offset, the
structure changes greatly when the offset is adjusted using the gain command of
XSPEC. However, the adjustment should be kept to be within ~10 eV. The
structure around 0.5 keV which changes greatly with an adjustment of the offset
is most probably an artifact.

2.3 Other calibration targets

It is suspected that the energy spectrum of 3C273 is not intrinsically a power
law but has a soft excess. The soft excess is probably not detected by GIS.
If the soft excess made a significant contribution in the ASCA SIS energy band
when the calibration observations of 3C273 were made, the current low energy
SIS calibration may have systematic errors. Thus, independent calibrations of
the low energy response should be useful. For this purpose, we analyzed the
data on 3C58 and the Coma cluster of galaxies. The analysis was done using the
FTOOLS version 3.4 or earlier.

3C58 is a Crab-like SNR and the energy spectrum is believed to obey a power
law. It has a relatively small absorption column (for SNR) and, of course, has
no time variability. 3C58 was so far observed with various satellites
including Einstein, EXOSAT, and Ginga. Thus the photon index is relatively
well constrained (above ~2 keV). The ROSAT PSPC data were found to be not
useful because of a gain problem.

Figure 6: The best fit photon index
and the equivalent hydrogen column density (NH) of 3C58 from various sets of
data. Contours are 90% confidence region obtained with the combined data of
Einstein SSS, Einstein MPC and Exosat. Ginga LAC gives only the upper limit of
NH. Error bars of the best fitting values of SIS and GIS are 90% confidence
limit for a single parameter. The neutral hydrogen column density obtained
from21cm measurements is 0.65 x 1022 cm-2.

ASCA observations of 3C58 were made in September 1995. Data were obtained for
3 chips (chips 0, 1, 2 for SIS-0 and chips 0, 2, 3 for SIS-1) and the 4th
pointing was used to obtain background data. The energy spectra were
calculated for each chip, and a power law model modified by an absorption was
fitted. The results are shown in figure 6 together with those of the previous
results. The finite source size was taken into account in making the ARF file,
but has little effects on the photon index and NH.

The hydrogen column density values obtained from the ASCA data are in general
slightly larger than the Einstein + EXOSAT and the Ginga values. GIS and SIS-0
give almost the same column density, but SIS-1 prefers a slightly higher value.
Several reasons are conceivable for the slightly higher NH obtained with ASCA:
(1) the energy spectrum of 3C58 may deviate from a power law below ~2 keV, (2)
the abundance of the absorbing material in the line of sight to 3C58 may not be
solar, (3) dust scattering may modify the apparent shape of the spectrum, or
(4) the contamination on XRT may have modified the response. As for the slight
difference of the parameters between SIS-0 and SIS-1, there are also several
possible origins: (1) a calibration error of the thickness of the absorption
layer (the thermal shield, the optical blocking filter, and the dead layer of
CCD), (2) a calibration error in the depletion layer of CCD, (3) a difference
in the radiation damage, (4) a difference in the optical light leak, or (5) a
calibration error of the position of the optical axis. Our current
understanding of the detector characteristics is not advanced enough to
distinguish the various possibilities. The SIS calibration currently in
progress is expected to clarify the origin of these differences.

The residual structure around 0.5 keV was investigated with the data of the
Coma cluster of galaxies (A1656). Coma cluster has a relatively high
temperature of ~10 keV and a low Galactic absorption (0.9 x 1020
cm-2). Thus it is expected to have a relatively simple spectrum of
lower energies. The data were obtained in June 1993. The model energy
spectrum used to fit the data is a Raymond-Smith model modified by the Galactic
absorption. The Galactic absorption (0.9 x 1020 cm-2)
and the red shift (z = 0.0235) were fixed in the course of the model fitting.
We found that the residual structure around 0.5 keV show large variations from
chip to chip and there was no clear systematic trend. The amplitude of the
residual structure was at most ~10% level. If we let the absorption be free in
the fitting, the best fit value increased for some chips by about 2 x
1020 cm-2. Thus, we consider that current estimate of
hydrogen equivalent column density has a systematic error of about 2 x
1020 cm-2.

2.4 Future calibration

The calibration of the SIS with 3C273, XRT and GIS responses have been updated.
Furthermore, introduction of a so-called "filter file" is planned to reduce the
systematic structures seen in the residuals of the GIS Crab spectrum. As
explained in figure 4, SIS (+XRT) calibration was done to give consistent
results with GIS (+XRT). Thus, once the XRT or GIS responses are revised, the
SIS calibration should be re-done with the new responses. Re-calibration of
SIS with the latest XRT and GIS responses (and "arf filter") is now under
way.

The previous calibration of the SIS was based on the assumption that the energy
spectrum of 3C273 can be well approximated by a power law modified by the
Galactic absorption. However, this assumption may not be correct. There may be
soft excess over the power law in the soft energy band. The soft excess seems
to be time variable, and hence it may not be easy to incorporate the soft
excess into the calibration. Possible systematic errors in the response due to
the soft excess will be evaluated in the near future.

3 Non-uniform Charge Transfer Inefficiency (CTI)

The CTI has gradually been increasing since the launch of ASCA. It had been
assumed to be uniform over a CCD chip, but a detailed analysis of recent data
showed that the CTI is now significantly non-uniform. In this section, we
explain the analysis we have done on the uniformity of CTI and its impact on
the SIS response. Energy resolution degradation due to the non-uniform CTI is
incorporated in the SIS response from FTOOLS version 3.5.

3.1 CTI measurements with Cas A data in 1995

We observed Cas A at 4 different pointing positions on the standard chips in
August 1995. Because this is more than the minimum number of 3 pointings
necessary to calculate parallel and serial CTI, we could check the uniformity
of CTI. The number of pointings on standard chips were 2 in 1993 and 3 in
1994. Thus, such an analysis became possible for the first time in 1995.

Figure 7: The pointing positions on the standard chips in 1995 Cas
observations. Using these 4 pointings of data, we can determine two parallel
CTIs, Cp1 and Cp2, independently.

Using these data we can determine parallel CTI at two different regions. One
is between o and h and the other is between v and x. We first
calculated the difference of apparent line energies between the pointing
positions using Si, S, Fe lines. We then calculated the CTI assuming if is
constant against photon energy, i.e. charge lost by CTI is proportional
to the original charge packet size. For example, Cp1 is calculated from the
line energy differences between v and x, and Cp2 from the line
energy differences between o and h. The results are listed in
table 1. Expected CTIs, which are extrapolated from the CTI determined by Cas
A data in 1994, are also listed in the table.

Errors are in 90% confidence limit.
Extrapolated CTI from the value in July 1994.

As seen from table 1, the difference of parallel CTIs with position, Cp1 and
Cp2, are large. The serial CTIs are also very different from the extrapolated
values based on 1994 measurements. This is because the serial CTI in 1994
measurement was determined under the assumption of uniform parallel and serial
transfer (ST) CTI (CTI associated with ST clock i.e., charge transfer from the
imaging to frame store area), which is not the case. Even for the serial CTI
determined from 1995 observations, the uniformity of the ST CTI is still
assumed. If the ST CTI is not uniform over the chip, which is very plausible,
serial CTI may be different from the value listed in the table. Because the
number of transfers associated with the ST CTI is constant (422) for all the
pixels in a chip, there is no way of directly measuring the ST CTI. According
to the investigation above, it is suspected that non-uniformity of CTI is very
large and may be comparable to the mean CTI.

3.2 Column to column variations of parallel CTI

The Cas A observation at the position of the standard chips has a relatively
long exposure to obtain enough statistics for the iron line. This means that
more than enough photons are available for the Si line. We can accumulate
energy spectra with good statistics if we select events from a single column
which lies under the brightest part of Cas A. Thus we can study column to
column variations of the energy spectra. We calculated the energy spectra with
grade 0 events of both the Bright mode data and the DFE-corrected Faint data.
The Bright mode data were obtained during satellite night time, and hence the
DFE stable. We show in Figure 8 the Si line energies calculated from the
spectra constructed from single column data. The H-addresses (RAWX) of the
columns are 344--353 for S0C1 and 380--389 for S1C3. Thus the data cover 10
consecutive columns, which correspond to 1/4 arcmin. This is much smaller
than the HPD of XRT and the change of spectral parameters should have
instrumental origin (not intrinsic to the source).

Figure 8: The Si line energies obtained from the single column energy
spectra. The variations of the line center energies are due to the column to
column variations of parallel CTI.

The standard deviations of the line center energies shown in Figure 8 are 22 eV
for S0C1 and 48 eV for S1C3. Because the line center shift due to the parallel
CTI is roughly 20 eV, this means that the relative variations of the parallel
CTI from column to column amount to 100%.

3.3 History of the Cas A line profile

The current CTI correction method assumes that CTI is uniform over a chip. The
non-uniformity of CTI means that the current CTI correction method cannot
restore the original energy resolution. This effect may be observed in the Cas
A spectra. The Cas A data were taken in various modes with various pointing
positions, but 1-CCD faint mode data were taken every year from the standard
chips at exactly the same pointing position as a reference. We show in Figure
9 the energy spectra calculated from these reference data, which were obtained
in August 1993, July 1994 and August 1995. The standard data selection was
applied and the data were corrected for DFE, echo and CTI. The CTI values used
are those determined from Cas A data in 1994 (2). Note that the RDD effect is
negligible for 1 CCD data.

Figure 9: The Cas A spectra in: August 1993, July 1994 and August 1995
showing the degradation in energy resolution. The spectra were calculated from
the data in 1-CCD Faint mode and were corrected for DFE and CTI.

As seen from figure 9, the degradation of the energy resolution is clear. This
is due to the non-uniformity of the CTI.

3.4 Degradation of energy resolution

We calculated the widths of Si, S and Fe lines of Cas A as a function of
observation time to evaluate the energy resolution degradation. The data used
here are basically the same as those shown in figure 9. All these data were
taken at the same pointing position of the standard chips, and were corrected
for DFE and echo. The lines are intrinsically broad and hence line width has
little intrinsic meaning. Measured line widths of Si, S and Fe are listed in
table 2.

We show in table 2 the line widths obtained before and after CTI correction.
As seen from the table, CTI correction does not improve the energy resolution.
This confirms that non-uniformity of CTI is very large and the small scale CTI
variations are comparable to the CTI itself.

3.5 Empirical model

The energy resolution degradation due to the non-uniform CTI can be modeled as
a change in the Fano factor with time. It is known that the statistical
fluctuation of the number of electrons produced by an X-ray photon is smaller
than that expected from the Poisson fluctuations. The Fano factor defines the
size of fluctuation in comparison with the Poisson fluctuation. We assume that
the Fano factor (f) changes linearly with time:

(3)

where
is the Fano factor at launch time,
Fano factor variation coefficient (s^-1), t
time after the launch (sec). With this assumption, the apparent line width in
in eV can be represented as follows:

(4)

where
is the intrinsic line width (eV), E line energy (eV). It has been found that
this model function can reproduce the observed history of the Si, S, Fe line
widths quite well. The best fit coefficients we have obtained are
sec-1 for SIS-0 and
sec-1 for SIS-1. The best fit model functions are shown in Figure
10 with the observed line widths.

Figure 10: The time variations of the apparent line widths of Cas A and
the best fit model function. The circles represent CTI correction data and the
triangles represent data not corrected for CTI. The model function is fitted
to the CTI-corrected data. The ASCA time at the launch is 0.432x10^7
sec.

The non-uniformity of the CTI is very large even on a microscopic scale in a
chip, and hence it is suspected that the CTI fluctuates even from pixel to
pixel. This means that, if we want to correct for CTI, we need to define the
CTI for each pixel. This is equivalent to defining the gain for each pixel and
hence practically impossible for SIS. Therefore, the only method we can apply
is to include the energy resolution degradation due to the non-uniform CTI in
the response matrices of SIS. This is done from the FTOOLS version 3.5 with
the above model of the Fano factor.